Question

Perform the following using shifting in 8-bit representations:

a. (50)10 * (4)10
b. (-102)10/(2)10

Answer 1

Using 8-bit binary shifting, 50 multiplied by 4 results in 200, and -102 divided by 2 results in -51. Left shifting multiplies by 2, and right shifting divides by 2.

Step-by-step explanation:

The question asks to perform operations using binary shifting for multiplication and division in 8-bit representation. Binary shifting to the left multiplies a number by 2 for each shift while shifting to the right divides a number by 2 for each shift.

a. (50)10 * (4)10: To multiply 50 by 4 using binary shifting, we convert 50 to binary, which is 00110010 in 8-bit representation, and then shift left by 2 bits (since 4 is 22), resulting in 11001000, which is 200 in decimal.

b. (-102)10 / (2)10: To divide -102 by 2 using binary shifting, we first represent 102 in 8-bit two complement form, which is 10011010, and then shift it right by 1 bit, to get 11001101, which is -51 in decimal.